Principal axis line simplification

Abstract

Line simplification is a basic spatial operator used to generalize the geometry of cartographic data. Many algorithms have been developed to simplify encoded lines using a bandwidth criterion that ensures that all of the originally encoded points are within a given distance tolerance of the resulting line caricature. This approach to line simplification derives from Peucker's theory of cartographic lines in which the spatial frequency of lines is represented by varying bandwidths around a center line. In this manner, line simplification is the elimination of high-frequency bandwidths through a spatial filtering process. Most of bandwidth algorithms force the endpoints of the center lines comprising the simplified line to correspond to selected points from the original encoding. An algorithm is presented here that focuses on an alternative bandwidth proposed by Peucker allowing the center line to pass through the “true” center of the set of points as measured by the sum of squared perpendicular distances between the center line and this set of points. Such a center line corresponds to the major axis of a two-dimensional point distribution in principal component analysis. Results show that line simplification using this criterion is computationally faster and results in fewer points retained for a given bandwidth than the traditional approach exemplified by the Douglas-Peucker algorithm.